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# What Are The Prime Factors Of 84

What are the prime factors of 84? Answer: 2, 3, 7

The number 84 has 3 prime factors. Primes can only have two factors(1 and itself) and only be divisible by those two factors. Any figure where this rule applies can be called a prime factor. The biggest prime factor of 84 is 7. The smallest prime factor of 84 is 2.

## What Is The Factor Tree Of 84

How to use a factor tree to find the prime factors of 84? A factor tree is a diagram that organizes the factoring process.

• First step is to find two numbers that when multiplied together equal the number we start with.
84
↙ ↘
2 × 42
• Second step is to check the multiplication(of the first step) for numbers that are not primes.
42
↙ ↘
3 × 14
• Third step is to check the multiplication(of the second step) for numbers that are not primes.
14
↙ ↘
7 × 2

We found 3 prime factors(2, 3, 7) using the factor tree of 84. Now let us explain the process to solving factor trees in more detail. Our goal is to find all prime factors of a given whole number. In each step of our factor tree diagram for 84 we always checked both multiplication numbers if they were primes or not. If one or both of the integers are not prime numbers then this means that we will have to make diagrams for them too. This process continues until only prime numbers are left.

Remember that often a factor tree for the same integer can be solved in more than one correct way! An example of this is the figure 12 where 2*6=12 and 4*3=12. The primes of a factor tree for 12 are the same regardles if we start the factor tree with 2*6 or 4*3.

## How To Verify If Prime Factors Of 84 Are Correct Answers

To know if we got the correct prime factors of 84 we have to get the prime factorization of 84 which is 2 * 2 * 3 * 7. Because when you multiply the primes of the prime factorization the answer has to be equal with 84.

After having checked the prime factorization we can now safely say that we got all prime factors.

## General Mathematical Properties Of Number 84

84 is a composite number. 84 is a composite number, because it has more divisors than 1 and itself. This is an even number. 84 is an even number, because it can be divided by 2 without leaving a comma spot. This also means that 84 is not an odd number. When we simplify Sin 84 degrees we get the value of sin(84)=0.73319032007329. Simplify Cos 84 degrees. The value of cos(84)=-0.68002349558734. Simplify Tan 84 degrees. Value of tan(84)=-1.078183805164. When converting 84 in binary you get 1010100. Converting decimal 84 in hexadecimal is 54. The square root of 84=9.1651513899117. The cube root of 84=4.3795191398879. Square root of √84 simplified is 2√21. All radicals are now simplified and in their simplest form. Cube root of ∛84 simplified is 84. The simplified radicand no longer has any more cubed factors.

## Determine Prime Factors Of Numbers Smaller Than 84

Learn how to calculate primes of smaller numbers like:

## Determine Prime Factors Of Numbers Bigger Than 84

Learn how to calculate primes of bigger numbers such as:

## Single Digit Properties For Number 84 Explained

• Integer 8 properties: Eight is even and a cube of 2. It is a composite, with the following 4 divisors:1, 2, 4, 8. Since the total of the divisors(excluding itself) is 7<8, it is a defective number. The sixth of the Fibonacci sequence, after 5 and before 13. It is the quantity of the twin primes 3 and 5. The first octagonal value. 8 is a Ulam, centered heptagonal and Leyland number. All amounts are divisible by 8 if and only if the result formed by its last three digits is. A refactorizable, being divisible by the count of its divisors. At the same time a highly totter and highly cototent quantity. It is the fourth term of the succession of Mian-Chowla. Any odd greater than or equal to 3, elevated to the square, to which subtract is subtracted 1 is divisible by 8 (example: 7²=49 49-1=48 divisible by 8). The sum of two squares, 8=2²+2². The sum of the digits of its cube: 8³=512, 5+1+2=8. The first 4-digit binary:1000. Part of the Pythagorean triples (6, 8, 10), (8, 15, 17). Eight is a repeated number in the positional numbering system based on 3 (22) and on the base 7 (11).
• Integer 4 properties: 4 is even and the square of 2. Being a composite it has the following divisors:1, 2, 4. Since the sum of the divisors(excluding itself) is 3<4, it is a defective digit. A highly composed, highly totter and highly cototent integer. In mathematic terms four is a component of Ulam, tetrahedral and a part of the Tetranacci Succession. The complete Harshad, which is a number of Harshad in any expressed base. A strictly non-palindrome. The third term of the succession of Mian-Chowla. In the numerical decimal system it is a Smith numeral. A figure is divisible by 4 if and only if its last two digits express a number divisible by four. Each natural value is the sum of at most 4 squares. 4 belongs to the first Pythagorean terna(3,4,5). The fourth issue of the succession of Lucas, after 3 and before 7. Four is a palindrome and a repeated digit in the 3-based positional numbering system.

## Finding All Prime Factors Of A Number

We found that 84 has 3 primes. The prime factors of 84 are 2, 3, 7. We arrived to this answer by using the factor tree. However we could have also used upside down division to get the factorization primes. There are more that one method to factorize a integer.

## List of divisibility rules for finding prime factors faster

Rule 1: If the last digit of a figure is 0, 2, 4, 6 or 8 then it is an even number. All even numbers are divisible by 2.

Rule 2: If the sum of digits of a integer is divisible by 3 then the figure is also divisible by 3 and 3 is a prime factor(example: the digits of 12 are 1 and 2 so 1+2=3 and 3 is divisible by 3, meaning that 12 is divisible by 3). The same logic also works for 9.

Rule 3: If the last two digits of a number are 00 then this integer is divisible by 4(example: we know that 124=100+24 and 100 has two zeros in the end making it divisible with 4. We also know that 4 is divisible with 24). In order to use this rule to it's fullest it is best to know multiples of 4.

Rule 4: If the last digit of a number is 0 or 5 then 5 it is divisible by 5.

Rule 5: All integers that are divisible by both 2 and 3 are also divisible by 6. This is logical because 2*3=6.

## What Are Prime Factors Of A Number?

All numbers that are only divisible by one and itself are called prime factors in mathematics. A prime factor is a figure that has only two factors(one and itself).